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Physical Review A

Multipole transitions of Rydberg atoms in modulated ponderomotive potentials

Brenton Knuffman, Georg A. Raithel

Published May 1, 2007• 25 citations
Publisher

Abstract

We consider multipole transitions between Rydberg states in amplitude-modulated standing-wave ponderomotive potentials. For experimentally realizable depths of the ponderomotive potential, we find Rabi frequencies of tens of kilohertz. The transitions are not subject to dipole selection rules and allow for changes in the angular momentum quantum number up to about 5. The effects of energy level shifts caused by the ponderomotive potential are discussed.

DOI
10.1103/physreva.75.053401

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Sep 10, 2010•1 citation
We consider multipole transitions between Rydberg states in amplitude-modulated standing-wave ponderomotive potentials. For experimentally realizable depths of the ponderomotive potential, we find Rabi frequencies of tens of kilohertz. The transitions are not subject to dipole selection rules and allow for changes in the angular momentum quantum number up to about 5. The effects of energy level shifts caused by the ponderomotive potential are discussed.
In ponderomotive spectroscopy an amplitude-modulated optical standing wave is employed to probe Rydberg-atom transitions, utilizing a ponderomotive rather than a dipole-field interaction. Here, we engage nonlinearities in the modulation to drive dipole-forbidden transitions up to the fifth order. We reach transition frequencies approaching the sub-THz regime. We also demonstrate magic-wavelength conditions, which result in symmetric spectral lines with a Fourier-limited peak at the line center. Applicability to precision measurement is discussed.
In ponderomotive spectroscopy an amplitude-modulated optical standing wave is employed to probe Rydberg-atom transitions, utilizing a ponderomotive rather than a dipole-field interaction. Here, we engage nonlinearities in the modulation to drive dipole-forbidden transitions up to the fifth order. We reach transition frequencies approaching the sub-THz regime. We also demonstrate magic-wavelength conditions, which result in symmetric spectral lines with a Fourier-limited feature at the line center. Applicability to precision measurement is discussed.
In this thesis, we examine the ponderomotive interaction between an applied optical field and a highly excited Rydberg electron. An atom in a Rydberg state is essentially composed of an electron loosely bound, at a relatively large radial separation, to a positive ionic core. As such, the ponderomotive interaction for the Rydberg electron is similar to the interaction with free charges, which has been studied in context of plasma physics, new particle accelerator techniques, ion trapping, and electron diffraction among others. We are focused on using the ponderomotive interaction with the Rydberg electron to exert control over both the center-of-mass and electronic states of translationally cold Rydberg atoms. These capabilities can be adapted as tools for application in many experiments in areas such as atomic spectroscopy and quantum information processing. Our theoretical investigations have provided a well-defined parameter space for our experimental work and have allowed us to develop experimental methods appropriate for studying Rydberg atoms in ponderomotive potentials. In dense gases of cold Rydberg atoms, rich dynamics stem from electric multipole interactions among the Rydberg atoms. For example, interatomic forces between Rydberg atoms cause state-changing collisions which can significantly increase the kinetic energy of the colliding atoms. In addition to the studies of Rydberg atoms in ponderomotive potentials, we discuss collisions of cold Rydberg atoms in which internal energy of the Rydberg atoms is converted into kinetic energy.
Dipole-dipole interactions between helium atoms in Rydberg-Stark states with principal quantum number n=53n=53n=53 and approximately linear Stark energy shifts, resulting from induced electric dipole moments of approximately 7900 D, have been investigated experimentally. The experiments were performed in pulsed supersonic metastable helium beams, with particle number densities of up to $\ensuremath{\sim}{10}^{9}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$. In the presence of amplitude-modulated, radio-frequency electric fields, changes in the spectral intensity distributions associated with the transitions to these states that are attributed to dipole-dipole interactions within the ensembles of excited atoms have been observed. The experimental results are in excellent agreement with calculations of the Rydberg energy level structure carried out using Floquet methods, and excitations shared by up to four atoms. The use of these Rydberg-Stark states as sensors for nonresonant broadband radio-frequency electrical noise is also discussed.
We develop and demonstrate a spectroscopic method for Rydberg-Rydberg transitions using a phase-controlled and -modulated, standing-wave laser field focused on a cloud of cold ^{85}Rb Rydberg atoms. The method is based on the ponderomotive (A^{2}) interaction of the Rydberg electron, which has less-restrictive selection rules than electric-dipole couplings, allowing us to probe both nS_{1/2}→nP_{1/2} and nS_{1/2}→(n+1)S_{1/2} transitions in first order. Without increase in laser power, third- and fourth-order subharmonic drives are employed to access Rydberg transitions in the 40 to 70 GHz frequency range using widely available optical phase modulators in the Ku band (12 to 18 GHz). Measurements agree well with simulations based on the model we develop. The spectra have prominent Doppler-free components with linewidths ≲200 kHz. The method paves the way for optical Doppler-free high-precision spectroscopy of Rydberg-Rydberg transitions and for spatially selective qubit manipulation with μm-scale resolution in Rydberg-based simulators and quantum computers, provided that magic states are chosen and that the atoms are sufficiently cold.
We study Rydberg atoms in ponderomotive optical lattices. Unlike for ground-state atoms, for Rydberg atoms in an optical lattice the extent of the electronic wave-function can approach the lattice period. This leads to state-dependent adiabatic trapping potentials that are unique to Rydberg atoms. We first discuss a theoretical model of adiabatic lattice potentials of Rydberg atoms. Then, we use microwave spectroscopy to experimentally demonstrate and investigate the state-dependence of the adiabatic potentials of S1/2 Rydberg states of rubidium. The observed microwave spectra depend strongly on both the principal quantum number and the depth of the lattice. A semi-classical simulation is used to explain the features seen in the spectra. Based on the results, we estimate the trapping efficiency of the ponderomotive optical lattice.